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# Multiple choice question for engineering

## Set 1

1. For a transistor amplifier to be stable, either the input or the output impedance must have a real negative part.
a) True
b) False

Answer: a [Reason:] For a transistor amplifier to be stable, either the input or the output impedance must have a real negative part. This would imply that │Гin│>1 or │Гout│>1, because these reflection coefficients depend on the source and load matching network.

2. ____________ condition, if met then the transistor can be impedance matched for any load.
a) Conditional stability
b) Unconditional stability
c) Infinite gain
d) Infinite input impedance

Answer: b [Reason:] A network is said to be unconditionally stable if │Гin│<1 and │Гout│<1 for all passive source and load impedance. Transistors that are unconditionally stable can be easily matched.

3. A network is said to be conditionally stable if:
a) │Гin│<1, │Гout│<1.
b) │Гin│>1, │Гout│>1
c) │Гin│>1, │Гout│<1
d) │Гin│<1, │Гout│>1

Answer: a [Reason:] For conditional stability, the condition to be satisfied is │Гin│<1, │Гout│<1. But this condition will be valid only for a certain range of passive source and load Impedance. His condition is also called potentially unstable.

4. Stability condition of an amplifier is frequency independent and hence can be operated at any frequency.
a) True
b) False

Answer: a [Reason:] Stability condition of an amplifier is frequency dependent since the input and output matching networks generally depend on frequency. Hence it is possible for an amplifier to be stable at the designed frequency and unstable at other frequencies.

5. For a unilateral device condition for unconditional stability in terms of S parameters is:
a) │S11│<1, │S22│<1
b) │S11│>1, │S22│>1
c) │S11│>1, │S22│<1
d) │S11│<1, │S22│>1

Answer: a [Reason:] For a unilateral device, the condition for unconditional stability is │S11│<1, │S22│<1. S11 parameter signifies the amount of power reflected back to port 1, which is the input port of the transistor. If this S parameter is greater is than 1, more amount of power is reflected back implying the amplifier is unstable.

6. If │S11│>1 or │S22│>1, the amplifier cannot be unconditionally stable.
a) True
b) False

Answer: a [Reason:] If │S11│>1 or │S22│>1, the amplifier cannot be unconditionally stable because we can have a source or load impedance of Zₒ leading to Гs=0 or ГL=0, thus causing output and input reflection coefficients greater than 1.

7. For any passive source termination ГS, Unconditional stability implies that:
a) │Гout│<1
b) │Гout│>1
c) │Гin│<1
d) │Гin│>1

Answer: a [Reason:] Unconditional stability implies that │Гout│<1 for any passive source termination, Гs. The reflection coefficient for passive source impedance must lie within the unit circle of the smith chart, nd the other boundary of the circle is written as Гs=e.

8. The condition for unconditional stability of a transistor as per the K-∆ test is │∆│> 1 and K<1.
a) True
b) False

Answer: b [Reason:] The condition for unconditional stability of a transistor is │∆│< 1 and K>1. Here, │∆│ and K are defined in terms of the s parameters of the transistor by defining the S matrix. To determine the unconditional stability of a transistor in K-∆ method, the S matrix of the transistor must be known.

9. If the S parameters of a transistor given are
S11=-0.811-j0.311
S12= 0.0306+j0.0048
S21=2.06+j3.717
S22=-0.230-j0.4517
Then ∆ for the given transistor is:
a) 0.336
b) 0.383
c) 0.456
d) None of the mentioned

Answer: a [Reason:] Given the S parameters of a transistor, the ∆ value of the transistor is given by │S11S22-S12S21│. Substituting the given values in the above equation, the ∆ of the transistor is 0.336.

10. By performing the K-∆ test for a given transistor the values of K and ∆ were found to be equal to 0.383 and 0.334 respectively. The transistor with these parameters has unconditional stability.
a) True
b) False

Answer: b [Reason:] The condition for unconditional stability of a transistor is │∆│< 1 and K>1. Here, │∆│ and K are defined in terms of the s parameters of the transistor by defining the S matrix. Here │∆│< 1 but the second condition is not satisfied. Hence they are not unconditionally stable.

## Set 2

1. Which mode of propagation is supported by a strip line?
a) TEM mode
b) TM mode
c) TE mode
d) None of the mentioned

Answer: a [Reason:] Since a stripline has 2 conductors and a homogeneous dielectric, it supports a TEM wave, and this is the usual mode of operation.

2. The higher order wave guide modes of propagation can be avoided in a strip line by:
a) Restricting both the ground plate spacing and the sidewall width to less than λd/2
b) Restricting both the ground facing plate spacing and the sidewall width to less than λd
c) Filling the region between 2 plates with di electric
d) Restricting both the ground plate spacing and the sidewall width between λg and λg/2

Answer: a [Reason:] When stripline is used as a media for propagation, it is always preferred that only certain modes of propagation are allowed. Hence, in order to avoid the higher order modes, it is achieved by restricting both the ground plate spacing and the sidewall width to less than λd/2.

3. Stripline can be compared to a:
a) Flattened rectangular waveguide
b) Flattened circular waveguide
c) Flattened co axial cable
d) None of the mentioned

Answer: c [Reason:] A stripline has an enter conductor enclosed by an outer conductor and are uniformly filled with a dielectric medium, these are similar to a coaxial cable. Hence it can be compared to a flattened coaxial cable.

4. If the dielectric material filled between the round plates of a microstrip line has a relative permittivity of 2.4, then the phase velocity is:
a) 1.3*108 m/s
b) 1.9*108 m/s
c) 3*108 m/s
d) 2*108 m/s

Answer: b [Reason:] Phase velocity is given by the expression C/√∈ for a stripline. Substituting the given values, the phase velocity for the above case is 1.9*108 m/s.

5. Expression for propagation constant β of a strip line is:
a) ω(√µ∈∈r)
b) ω(√µₒ/√∈r)
c) ω/(√µₒ∈ₒ∈r)
d)c/(√µₒ∈ₒ∈r)

Answer: a [Reason:] Propagation constant is associated with the propagating wave in the strip line. This propagation constant for a wave is defined by the expression ω(√µ∈∈r).

6. If the phase velocity in a stripline is 2.4*108m/s, and the capacitance per unit length of a micro stripline is 10pF/m, then the characteristic impedance of the line:
a) 50 Ω
b) 41.6 Ω
c) 100 Ω
d) None of the mentioned

Answer: b [Reason:] Characteristic impedance of a stripline is given by 1/ (vPc). Substituting the given values of phase velocity and capacitance, the characteristic impedance of the line is 41.6 Ω.

7. The expression for characteristic impedance Zₒ of a stripline is:
a) (30πb/√∈r)(1/We+0.441b)
b) (30πb) (1/We+0.441b)
c) 30π/√∈r
d) (1/We+0.441b)

Answer: a [Reason:] Characteristic impedance of a stripline is a function of the various parameters of the stripline. They are effective width, thickness and relative permittivity of the dielectric material. Changing any one of these parameters results in changing the characteristic impedance of the line The derived expression is hence (30πb/√∈r)(1/We+0.441b).

8. If the effective width of the center conductor is 3 mm and the distance between the two ground plates is 0.32 cm with the material of the dielectric used having a relative permittivity of 2.5, then what is the characteristic impedance of the strip line?
a) 50Ω
b) 71.071Ω
c) 43.24Ω
d) 121Ω

Answer: c [Reason:] The characteristic impedance of a stripline is given by the expression (30πb/√∈r)(1/We+0.441b). Substituting the given values in the given expression and hence solving, the characteristic impedance of the line is 43.24 Ω.

9. The wave number of a stripline operating at a frequency of 10 GHz is:
a) 401
b) 155
c) 206
d) 310

Answer: d [Reason:] The wave number of a microstrip line is given by the expression 2πf√∈r/c, c is the speed of light in space, ∈r is the relative permittivity of the dielectric medium. Substituting the given values in the equation, the wave number is 310.

10. If the loss tangent is 0.001 for a stripline operating at 12 GHz with the relative permittivity of the dielectric material being used equal to 2.6, then the conductor loss is:
a) 0.102
b) 0.202
c) 0.001
d) 0.002

Answer: b [Reason:] Conductor loss in a stripline is given by the expression k*tanδ/2. K is given by the expression 2πf√∈r/C which is the wave number. Substituting the values in the above two equations, conductor loss is 0.202.

11. If the dielectric material used between the grounded plates of a stripline is 2.2, when the strip line operating at 8 GHz, the wavelength on stripline is:
a) 1.2 cm
b) 2.52 cm
c) 0.15 cm
d) 3.2 cm

Answer: b [Reason:] The propagating wavelength on the stripline is defined by the relation C/f√∈r. substituting in the above relation, the propagating wavelength on the microstrip line is 2.52 cm.

12. Fields of TEM mode on strip line must satisfy:
a) Laplace’s equation
b) Ampere’s circuital law
c) Gaussian law
d) None of the mentioned

Answer: a [Reason:] If φ(x,y) is the function of potential in the stripline varying along the width and thickness, this potential function must satisfy the Laplace’s equation.

## Set 3

1. If an antenna has a directivity of 16 and radiation efficiency of 0.9, then the gain of the antenna is:
a) 16.2
b) 14.8
c) 12.5
d) 19.3

Answer: a [Reason:] Gain of an antenna is given by the product of radiation efficiency of the antenna and the directivity of the antenna. Product of directivity and efficiency thus gives the gain of the antenna to be 16.2.

2. Gain of an antenna is always greater than the directivity of the antenna.
a) True
b) False

Answer: b [Reason:] Gain of an antenna is always smaller than the directivity of an antenna. Gain is given by the product of directivity and radiation efficiency. Radiation efficiency can never be greater than one. So gain is always less than or equal to directivity.

3. A rectangular horn antenna has an aperture area of 3λ × 2λ. Then the maximum directivity that can be achieved by this rectangular horn antenna is:
a) 24 dB
b) 4 dB
c) 19 dB
d) Insufficient data

Answer: c [Reason:] Given the aperture dimensions of an antenna, the maximum directivity that can be achieved is 4π A/λ2, where A is the aperture area and λ is the operating wavelength. Substituting the given values in the above equation, the maximum directivity achieved is 19 dB.

4. A rectangular horn antenna has an aperture area of 3λ × 2λ. If the aperture efficiency of an antenna is 90%, then the directivity of the antenna is:
a) 19 dB
b) 17.1 dB
c) 13 dB
d) 21.1 dB

Answer: b [Reason:] Given the aperture dimensions of an antenna, the directivity that can be achieved is ap4π A/λ2, where A is the aperture area and λ is the operating wavelength, ap is the aperture efficiency. Substituting the given values in the above equation, the directivity achieved is 17.1 dB.

5. If an antenna has a directivity of 16 and is operating at a wavelength of λ, then the maximum effective aperture efficiency is:
a) 1.27λ2
b) 2.56λ2
c) 0.87λ2
d) None of the mentioned

Answer: a [Reason:] Maximum effective aperture efficiency of an antenna is given by D λ2/4π, D is the directivity of the antenna. Substituting in the equation the given values, the maximum effective aperture is 1.27λ2.

6. A resistor is operated at a temperature of 300 K, with a system bandwidth of 1 MHz then the noise power produced by the resistor is:
a) 3.13×10-23 watts
b) 4.14×10-15 watts
c) 6.14×10-15 watts
d) None of the mentioned

Answer: b [Reason:] For a resistor noise power produced is given by kTB, where T is the system temperature and B is the bandwidth. Substituting in the above expression, the noise power produced is 4.14×10-15 watts.

7. With an increase in operating frequency, the background noise temperature:
a) Increases
b) Decreases
c) Remains constant
d) Remains unaffected

Answer: a [Reason:] The plot of frequency v/s background noise temperature shows that with the increase of the signal frequency, the background noise temperature increases. Also, with the increase of the elevation angle from the horizon, background noise temperature increases.

8. The noise temperature of an antenna is given by the expression:
d) None of the mentioned

Answer: a [Reason:] The noise temperature of an antenna is given by the expression radTb + (1-rad) Tp. here, Tb is the brightness temperature and Tp is the physical temperature of the system. rad is the radiation efficiency. Noise temperature of a system depends on these factors.

9. Low is the G/T ratio of an antenna, higher is its efficiency.
a) True
b) False

Answer: b [Reason:] In the G/T ratio of an antenna, G is the gain of an antenna and T is the antenna noise temperature. Higher the G/T ratio of an antenna better is the performance of the antenna.

10._________ has a constant power spectral density.
a) White noise
b) Gaussian noise
c) Thermal noise
d) Shot noise

Answer: a [Reason:] Thermal noise has a power spectral density for a wide range of frequencies. Its plot of frequency v/s noise power is a straight line parallel to Y axis.

## Set 4

1. A single section tapered line is more efficient in impedance matching than a multisection tapered line for impedance matching.
a) True
b) False

Answer: b [Reason:] As the number N of discrete transformer sections increases, the step changes in the characteristic impedance between the sections become smaller, and the transformer geometry approaches a continuous tapered line. Thus multisection are preferred over single section for impedance matching.

2. Passband characteristics of tapered lines differ from one type of taper to another.
a) True
b) False

Answer: a [Reason:] The impedance of the tapered line varies along the line depending on the type of the tapering done. Thus impedance is a function of the type of taper. Hence passband characteristics depend on the type of taper.

3. For a continually tapered line, the incremental reflection co-efficient is:
a) ∆Z/2Z
b) 2Z/∆Z
c) ∆Z0/2Z0
d) None of the mentioned

Answer: a [Reason:] The incremental reflection co-efficient ∆Г is a function of distance. If a step change in impedance occurs for z and z+∆z, then the incremental reflection co-efficient is given by ∆Z/2Z.

4. The variation of impedance of an exponentially tapered line along the length of the line is given by:
a) Z(z)=Z0eaz
b) Z(z)=Z0e-az
c) Z(z)=Z0e2az
d) Z(z)=Z0e-2az

Answer: a [Reason:] The variation of impedance along the transmission line is a positive growing curve and is given by Z(z)=Z0eaz. The constant ‘a’ is defined as L-1 ln(ZL/Z0).

5. The value of constant ‘a’ for an exponentially tapered line of length 5 cm with load impedance being 100Ω and characteristic impedance of the line is 50Ω is:
a) 0.1386
b) 0.265
c) 0.5
d) 0.2

Answer: a [Reason:] The constant ‘a’ for a tapered transmission line is given by L-1 ln(ZL/Z0). ‘a’ is a function of the tapered length, load and characteristic impedance. Substituting the given values in the above expression, ‘a’ has the value 0.1386.

6. Reflection co-efficient magnitude response is an exponential curve for tapered line.
a) True
b) False

Answer: b [Reason:] The reflection co-efficient magnitude response of a exponential tapered line resembles only positive valued sinc function or can be called as a function with multiple peaks.

7. Triangular taper is the best solution for any impedance matching requirement.
a) True
b) False

Answer: b [Reason:] Klopfenstein taper is the best and most optimized solution for impedance matching because reflection co-efficient has minimum value in the passband.

8. The maximum passband ripple in a Klopfenstein taper matching section is:
a) Г0/cos h A
b) Г0/sin h A
c) Г0/ tan h A
d) None of the mentioned

Answer: a [Reason:] The maximum passband ripple in a Klopfenstein taper matching section is Г0/cos h A. Here, Г0 is the reflection co-efficient at zero frequency. A is a trigonometric function relating reflection co-efficient at zero frequency and maximum ripple in the passband.

9. For any load impedance, perfect match can be obtained and the minimum reflection co-efficient achieved can be zero.
a) True
b) False

Answer: b [Reason:] From Bode-Fano criterion, there is a theoretical limit on the minimum achievable reflection co-efficient for a given load impedance. Hence, perfect match cannot be obtained.

10. For a given load (a fixed RC product), a broader bandwidth can be achieved with a low reflection co-efficient in the passband.
a) True
b) False

Answer: b [Reason:] Based on the theoretical results of Bode-Fano criterion, a broader bandwidth can be achieved only at the expense of a higher reflection coefficient in the passband.

11. A perfect match can be obtained in the passband for any impedance matching circuit around the center frequency for which it is defined.
a) True
b) False

Answer: b [Reason:] The passband reflection co-efficient cannot be zero unless the bandwidth is zero. Thus a perfect match can be obtained only at a finite number of discrete frequencies.

## Set 5

1. When a lossless line is terminated with an arbitrary load impedance ZL, then it :
a) causes wave reflection on transmission lines
b) transmits the entire supplied power
c) causes loss in transmission line
d) none of the mentioned

Answer: a [Reason:] When a line is terminated with a impedance other the characteristic impedance of the transmission line, It results in reflection of waves from the load end of the transmission line hence resulting in wave reflection in the transmission line.

2. We say a transmission line is matched when:
a) ZL=Z0
b) ZL=√Z0
c) ZL=Z0/2
d) ZL=2Z0

Answer: a [Reason:] We say a line is matched only when the characteristic impedance of the transmission line is equal to the terminating load impedance. Hence condition for a line to be matched is ZL=Z0.

3. Voltage reflection coefficient can be defined as:
a) ratio of amplitude of reflected voltage wave to the transmitted voltage wave
b) ratio of amplitude of reflected voltage to the incident voltage wave
c) ratio of load impedance to the characteristic impedance of the transmission line
d) none of the mentioned

Answer: b [Reason:] From transmission line theory, reflection co-efficient of a transmission line is defined as the ratio of amplitude of reflected voltage to the incident voltage wave.

4. Expression for a voltage reflection co-efficient in terms of load impedance and characteristics impedance is:
a) (ZL– Z0)/(ZL+ Z0)
b) (ZL+ Z0)/(ZL– Z0)
c) ZL. Z0/( ZL+ Z0)( ZL-Z0)
d) (ZL+ Z0)( ZL-Z0)/ ZL. Z0

Answer: a [Reason:] The amplitude of the reflected voltage wave at the load end is equal to the difference between the load and the characteristic impedance, incident voltage is proportional to the sum of the load and characteristic impedance.

5. If a transmission line of a characteristics impedance 50 Ω is terminated with a load impedance of 100 Ω, then the reflection co efficient is:
a) 0.3334
b) 0.6667
c) 1.6
d) 1.333

Answer: a [Reason:] Expression for reflection co-efficient of a transmission line is (ZL– Z0)/(ZL+ Z0) .substituting the given values of load and characteristic impedance, we get reflection co-efficient equal to 0.3334.

6. Return loss for a transmission line in terms of its reflection co efficient is given by:
a) -20logl┌l in dB where ┌ is the reflection coefficient.
b) -10logl┌l in dB where ┌ is the reflection coefficient
c) -10log (1/l┌l) in dB where ┌ is the reflection coefficient
d) -20log (1/l┌l) in dB where ┌ is the reflection coefficient

Answer: a [Reason:] Return loss signifies the amount of energy reflected back from the load which is proportional to the reflection co-efficient of the line. Return loss in dB is given by the logarithm of the reflection co-efficient.

7. If the reflection coefficient for transmission line is 0.24, then the return lossin dB is:
a) 12.39dB
b) 15dB
c) -12.39dB
d) -15.2dB

Answer: a [Reason:] The return loss of a transmission line, given the reflection co-efficient is -20logl┌l in dB where ┌ is the reflection co-efficient. Substituting for reflection co-efficient in the above equation, return loss is 12.39dB.

8. Expression for VSWR in terms of reflection co-efficient is:
a) (1+│┌│)/(1-│┌│)
b) (1-│┌│)/(1+│┌│)
c) 1/│┌│
d) 1/1+│┌│

Answer: a [Reason:] VSWR is the ratio of maximum amplitude of the standing wave formed to the minimum amplitude of the standing wave, when these voltages are expressed in terms of reflection co-efficient, we get the expression(1+│┌│)/(1-│┌│).

9. If the reflection co-efficient for a transmission line is 0.3, then the VSWR is:
a) 0.5384
b) 1.8571
c) 0.4567
d) 3.6732